The White House and Speaker John A. Boehner exchanged barbs Thursday over the potential for a shutdown showdown this fall, underscoring the yawning budget gap between the parties that threatens to torpedo this year’s appropriations bills.

The House passed the first fiscal 2014 spending bills this week despite two veto threats, and the Senate is set to mark up funding measures in the coming weeks. But the two chambers are operating off vastly different numbers — given that the House and Senate haven’t come close to reaching a budget deal — setting the stage for another stopgap spending bill this fall and, theoretically, a shutdown fight if the two sides can’t agree.

The House is following a $967 billion spending level that assumes the budget sequester remains in effect. Senate Appropriations Chairwoman Barbara A. Mikulski, D-Md., has said she is moving forward at a $1.058 trillion level that operates on the idea Congress will find a fix for the sequester.

Her GOP counterpart, Sen. Richard C. Shelby of Alabama, said Appropriations Republicans in the Senate want to work off the House number.

“We’ve got a few problems,” an understated Shelby told CQ Roll Call in a brief interview, noting that the committee’s Republicans hadn’t yet decided on a strategy for the markups. “The bottom line is we’re going to stay with the figure, which is the lower figure, the House has agreed with.”

It was just that sort of dispute that seems to have prompted the administration’s unusually broad veto threat on Republican spending bills until there’s a budget agreement.

“In veto threats of two House spending bills — both of which passed with overwhelming support — the White House said the president would not sign any — any — spending bills unless we agree to his demands on a broader budget deal. In short, the president said give him higher taxes and higher spending or we’ll shut down the government,” Boehner said Thursday. “That’s reckless.”

Republican appropriators dismissed the veto threat earlier in the week, but Boehner said it violated his March 1 deal with the president to keep the appropriations bills separate from deficit talks. White House spokeswoman Amy Brundage responded to the Ohio Republican with some snark of her own.

“We were pleased to see Speaker Boehner hold a press conference today to announce the end of the Republican strategy of governing by crisis,” she said. “We look forward to seeing Republicans in Congress act responsibly to pay the bills they have already racked up, along with funding the government to avoid a government shutdown.” But she reiterated that the White House isn’t going to just go along with the Republican budget.

“Republicans are refusing to allow us to go to conference for one reason, and that’s because they want to force a manufactured crisis over the debt limit this fall, because they think it will give them leverage,” Murray said. “So let’s be clear about which side is reckless today. Democrats want to get to work right now.”

A number of Senate conservatives have called on Murray to disavow any attempt to raise the debt limit through reconciliation, which has contributed to a regular series of standoffs on the floor.

“That’s always a concern. You’ve got to stay within the numbers, and that’s our concern. We have a difference of about $90 billion between what we think and what the Democrats [think],” Shelby said.

There is a related concern among some lawmakers that the House is moving first on easier-to-pass bills (funding veterans, homeland security and the military), potentially increasing pressure in the months ahead to blow through the caps to pass more contentious domestic spending bills.

“My concern is that we don’t stick to ... the budget control agreement that we agreed to. That’s the concern of the House, and there’s some concern that the sequence of bills will ensure — that time-honored practice in the House — the way you sequence them means you bust the budget in the end,” Sen. Jeff Flake said on Wednesday. The Arizona Republican is a frequent critic of the appropriations process.

“That’s always been a concern in marking up appropriation bills. I mean, whichever ones go first tend to get into the money early and then ... the later bills get harder and harder to do,” said Sen. John Thune of South Dakota, a member of the Republican leadership.

Still, some appropriators maintained their optimism.

“I am hopeful that we’ll get a significant number of bills passed in the right way. I’m eager to see us get to the point where we’re passing all the bills in the right way,” Sen. Roy Blunt, R-Mo., said. “I hope we make real progress toward that goal this year, and I’m sure that Sen. Mikulski and Sen. Shelby share that.”

Iowa Democratic Sen. Tom Harkin, the longtime chairman of the Senate Labor, Health and Human Services and Education Appropriations Subcommittee who is responsible for what’s among the most difficult bills to pass, said he does not want to get stuck near the end of the line, which has happened in the past. Those departments have frequently operated on stopgap funding in lieu of a full appropriations measure.

“I hope we’re going to do Labor-H sooner rather than later,” Harkin said. “We’re not going to do it last this time.”